School officials presented two proposals Monday night for assigning students to schools that could bring back the closest thing Boston has had to neighborhood schools since before the days of desegregation.

The most dramatic proposal would scrap the notion of geographic attendance boundaries and cross-city busing by simply allowing students to attend the closest school to their home with available seats. The other proposal would carve the city ­into 23 attendance regions, giving most parents a choice of two, three, or four schools, while subdividing almost ­every neighborhood, including East Boston and West Roxbury.

“Today, we as a community face the most important and impactful decisions in the history of this city, and the complexity and urgency of this important work requires an unwavering and singular focus and a resolve to do what must be done to ensure all of our children’s future for generations to come,” Superintendent Carol R. Johnson told the advisory committee and about 200 parents, community activists, and others gathered at Lilla Frederick Pilot Middle School in Dorchester.

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All the proposals represent a big departure from the city’s 23-year-old system of assigning students to schools. The system, originally designed to comply with court-ordered ­desegregation, currently chops the city into three sprawling geographic regions and sometimes sends children who live on the same street to several schools many miles apart, driving up transportation costs and often pulling apart the fabric of neighborhood togetherness.

The proposed changes are an attempt by Menino to simplify the process for families to apply to schools, build a stronger sense of community in neighborhoods much more ­diverse than in the 1970s, and, it is hoped, reduce busing costs in a city that spends about $80 million a year to transport students to school.

The Boston Globe

Mayor Thomas M. Menino wanted students from the same neighborhoods to be able to study together.

Menino said at the meeting that redesigning the student-assignment system will yield schools that are more connected to their communities.

“Those children can be ­together, and they can work with each other on homework,” he said. “That’s what I’m thinking about. That’s what we want to get to.”

During the presentation, parents sat attentively, poring over the maps and occasionally speaking quietly among themselves. People who did speak during public comment tended to raise concerns about the lack of specifics on increasing ­access to good schools and the prospect of fewer choices.

“When I look at all of these maps . . . it seems that my ­options are limited in all of them,” said Meghan Doran, 30, a Roslindale mother of a 2-year-old.

The advisory committee will sort through the proposals, which could be tweaked, and will recommend one in November. The School Committee is then expected to vote on that recommendation in December. Changes could go into effect for fall 2014.

But building public support will be a mighty task. For more than a decade, the mayor and the School Department have repeatedly tried to overhaul the assignment system. But those efforts have repeatedly failed, amid concern that the city has too few high-performing schools to meet demand.

The proposals are already generating skepticism.

State Representative Marty Walz, a Boston Democrat, said she was disappointed that none of the proposals called for opening a school in the Back Bay, Beacon Hill, or West End areas of the city, which do not have a nearby school.

“This proposal fails to meet the needs of families in downtown neighborhoods because it does not allow them to go to a school close to their home,” Walz said in an interview.

Johnson acknowledged in her opening remarks that ­aspects of the proposals could require new schools or expansionof existing ones.

She also said the proposals will not guarantee that students will be able to attend a good school and said the School Department is working to overhaul academic programs and instruction, particularly at 21 schools that are running the risk of being identified as under­performing by the state.

The distance students could shave off from their commutes to school is quite striking under the zone-free map. Under that scenario, they would travel less than a quarter-mile, on average, compared with the current average of 1.49 miles.

But the proximity under that plan comes with a tradeoff: It would lead to the greatest segregation of students by race and class among the five proposals, and it runs the highest probability of sending many of the city’s poorest children of color to some of the worst-performing schools.

By contrast, poor students under the six-zone proposal would have a better chance of getting into a high-performing school than under the zone-free map.

But the average distance traveled to school would ­increase to 1.29 miles, representing a modest decrease from current levels.

The proposals could roughly save from 7 percent to 27 percent in transportation cost, depend­ing on the proposal, said Michael Goar, deputy ­superintendent.

He also said that no decisions have been made on whether students currently ­enrolled at schools could stay there and for how long after the student-assignment changes are made.

Megan Wolf, a Jamaica Plain parent, cautioned the panel against placing too much emphasis on proximity. She said studies indicate that “closer-­to-home schools don’t mean more integration, but less.”

One aspect of the student-assignment system that many parents loathe will not change under any of the proposals: having parents rank their choices of schools and then waiting many weeks to see if the School Department’s computer algorithm gives them their top pick or one of their less enthusiastic options.

But parents of elementary school students will not have to go through the process again for middle school anymore. Under the proposal, each elementary school would be designated to feed into a specific middle school.

The School Department will gather additional input from parents and other interested community members at a series of community meetings that kick off Thursday at 7 p.m. at the Burke High School in Dorchester.